In a large saucepan over medium heat, fry 4 strips of bacon until crisp. Discard bacon. Saute onions and shallots in bacon fat until tender, about 10 minutes. Add balsamic vinegar, wine and oregano; cook for 30 minutes. Stir frequently until the onions caramelize and are golden brown.
Blend in chicken broth. Simmer gently for 1 hour, stir occasionally. Season with salt and pepper. Ladle soup into 4 ovenproof bowls. Float the croutons on top of soup and sprinkle with grated cheese. Broil until cheese melts. Garnish with flat-leaf parsley, serve immediately.